channel cooling rate - rapid quenching

[rwilt1]

I have a micro-channel (part of an electrochemical flow cell) with a square cross-section 100um x 100um. The walls are glass (thermal conductivity = 1.05 W/m/K) of 1mm thickness. I want to be able to rapidly quench the flowing solution by immersing the channel in liquid nitrogen.

On immersion the inner wall temperature will be 298K, outer wall 77K. My first question is - How quickly will the inner wall reach the freezing point of the solution 229K (acetonitrile)?

Second - How long before the solution is stationary? (given thermal conductivity of acetonitrile = 0.188 W/m/K)

I am a chemist and would appreciate any guidance on how to approach this problem.

 

[25362]

I wonder whether this link may guide you to the answer you are after:

http://www.annalsnyas.org/cgi/content/abstract/858/1/262

Anyway, the problem deals with film boiling. It wouldn't hurt to re-check the thermal conductivity of the glass at the prevailing temperatures and consider also the length of the submerged channel.

 

[volpe2]

For a first pass, you can also try the lumped capacitance method. You can work it out on paper, and it will give you reasonable results. You will need to research what the convection constant (h = 5-25 W/M^2*C for free convection in electronincs) for acetonitrile to glass.